The elastic vibration of the wheelset is a potential factor inducing wheel-rail defects. It is important to understand the natural vibration characteristics of the flexible wheelset for slowing down the defect growth. To estimate the elastic free vibration of the railway wheelset with the multidiameter axle, the transfer matrix method (TMM) is applied. The transfer matrices of four types of elastic beam models are derived including the Euler–Bernoulli beam, Timoshenko beam, elastic beam without mass and shearing stiffness, and massless elastic beam with shearing stiffness. For each type, the simplified model and detailed models of the flexible wheelset are developed. Both bending and torsional modes are compared with that of the finite element (FE) model. For the wheelset bending modes, if the wheel axle is modelled as the Euler–Bernoulli beam and Timoshenko beam, the natural frequencies can be reflected accurately, especially for the latter one. Due to the lower solving accuracy, the massless beam models are not applicable for the analysis of natural characteristics of the wheelset. The increase of the dividing segment number of the flexible axle is helpful to improve the modal solving accuracy, while the computation effort is almost kept in the same level. For the torsional vibration mode, it mainly depends on the axle torsional stiffness and wheel inertia rather than axle torsional inertia.

中文翻译：

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基于传递矩阵法的多种弹性梁模型轮对自然振动特性估计

轮对的弹性振动是导致轮轨缺陷的潜在因素。了解柔性轮对的自然振动特性对于减缓缺陷增长很重要。为了估计具有多直径轴的铁路轮对的弹性自由振动，应用了传递矩阵法 (TMM)。推导出四种弹性梁模型的传递矩阵，包括欧拉-伯努利梁、铁木辛柯梁、无质量和剪切刚度的弹性梁和具有剪切刚度的无质量弹性梁。针对每种类型，开发了柔性轮对的简化模型和详细模型。弯曲和扭转模式都与有限元 (FE) 模型进行了比较。对于轮对弯曲模式，如果将轮轴建模为欧拉-伯努利梁和铁木辛科梁，则可以准确地反映自然频率，尤其是后者。由于求解精度较低，无质量梁模型不适用于轮对自然特性的分析。柔性轴分割段数的增加有助于提高模态求解精度，同时计算量几乎保持在同一水平。对于扭振模态，主要取决于车轴扭转刚度和车轮惯量，而不是车轴扭转惯量。柔性轴分割段数的增加有助于提高模态求解精度，同时计算量几乎保持在同一水平。对于扭振模态，主要取决于车轴扭转刚度和车轮惯量，而不是车轴扭转惯量。柔性轴分割段数的增加有助于提高模态求解精度，同时计算量几乎保持在同一水平。对于扭振模态，主要取决于车轴扭转刚度和车轮惯量，而不是车轴扭转惯量。